The last two times I tried to backup a Ninjhax save from the Gateway menu, both failed.

I am interested to know if a Cubic Ninja cartridge that has been used to access Gateway 3.1.1 on a N3DS, will work on an O3DS to start Gateway.

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It's right on their site:

NOTE: Support for launching the Gateway menu through Cubic Ninja or Zelda Ocarina of Time on the Classic 3DS is not implemented yet.
If we get enough interested users we will consider implementing it for the Classic 3DS too.

I was just wondering, maybe the QR code scanning only works for N3DS, but once the gateway-launching save file is in Cubic Ninja it may work for both N3DS and O3DS. Wishful thinking, as an owner of a browserless O3DS 8.1.0-0U